49584960 has 140 divisors (see below), whose sum is σ = 176474628. Its totient is φ = 13215744.

The previous prime is 49584943. The next prime is 49584961. The reversal of 49584960 is 6948594.

It is a happy number.

49584960 is a `hidden beast` number, since 4 + 9 + 584 + 9 + 60 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 31539456 + 18045504 = 5616^2 + 4248^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (49584961) by changing a digit.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 24964 + ... + 26876.

Almost surely, 2^49584960 is an apocalyptic number.

49584960 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 49584960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (88237314).

49584960 is an abundant number, since it is smaller than the sum of its proper divisors (126889668).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

49584960 is a wasteful number, since it uses less digits than its factorization.

49584960 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1942 (or 1923 counting only the distinct ones).

The product of its (nonzero) digits is 311040, while the sum is 45.

The square root of 49584960 is about 7041.6588954592. The cubic root of 49584960 is about 367.3809693644.

The spelling of 49584960 in words is "forty-nine million, five hundred eighty-four thousand, nine hundred sixty".